This route is more a scramble/adventure hike than a climbing proposition. It is however way cool and should be explored if you are ever in the vicinity of the Royal Arch.
Hike to the spring (hopefully you'll try this when it is dry) and hike West into the gaping cave under some chockstones held in place between the 4th Flatiron and the Lower Tangen tunnel. Climb into the cave and climb up a spiral staircase formed by large boulders, way cool!
This will eventually lead you to the top of the chockstones and into a small amphitheater nestled between the Tangen towers and the 4th Flatiron. This amphitheater is very vegetated and not by good weeds either, so watch out for the poison stuff. I did this in winter after the snow had melted, so the vegetation was dead and flatenned.
Once here, you have a choice to continue up some easy (class 4) slabs that will then place you just North of the 5th Flatiron. If you are into rough hiking you can continue up to the summit of Green mountain by squeezing between the 5th and Schmoe's Nose.
For less-adventurous folks looking to experience the tunnel only, as you emerge out of it, hike South via the saddle between the towers and then East back to the Royal Arch trail.
Following this route to the top of Green Mountain is in my opinion the single worst bushwhack in the Boulder area. I recommend exiting early and escaping via the col between the Tangen Towers. People training for the Eco-challenge should do the complete climb daily, however.
Possibly the worst bushwhack, but the only other people I have seen up there, besides hikers, on the Royal Arch Trail are those who I have brought along for the ride. The view from the top of the upper Tangen Tower is magnificent. It is also possible to use this route as access to the summit of the [Fourth] Flatiron. One might consider long pants for that maneuver, you might get all itchy. REAL itchy! There are also millions of little stickers.